We study the application of wavelet packet filterbanks to low bit-rate transparent audio coding, taking the audio coders' delay requirements into account, and propose low-delay coders based on wavelet packet filterbanks. We first develop a method of comparison between filterbanks for perceptual audio coding by estimating the necessary bit-rate for a transparent compression. We use this comparison method in order to select the best filters for our audio compression scheme, from a large set of orthogonal and biorthogonal wavelets. Different wavelet filters may be used at different stages of the tree-structured decomposition with a constraint on the overall delay taken into account. The optimization is carried out with a simulated annealing procedure, proposing two wavelet packet filterbanks, exhibiting average and low delays. They are inserted in a complete audio coder that employs vector quantization and considers psychoacoustic models. The use of the proposed filterbanks leads to the design of a new bit allocation procedure, taking into account the lack of selectivity of the equivalent synthesis filters in a wavelet packet filterbank. The resulting audio scheme is validated through listening tests. The wavelet packet filterbanks are shown to be a promising tool for audio coding, especially for low-delay coding: with average delay, the quality of the wavelet packet filterbanks is as good as with MPEG-1 Layer-2, both with 80 kb/s, and when reducing the delay to 200 samples, 96 kb/s are needed to achieve the same quality.

The energy preservation property is among the most widely used properties of orthogonal transforms in image compression because the reconstruction error can be computed as the sum of the subband distortions. Thus, this is a key point in the use of efficient bit allocation techniques such as rate-distortion algorithms. Therefore, we study the nonorthogonality of biorthogonal filterbanks with reference to energy preservation from both theoretical and applicative points of view. We calculate the Riesz bounds as energy preservation bounds for filterbanks and discrete wavelet transforms, and then connect these results with the Riesz bounds of the related continuous wavelet transform. The simultaneous use of biorthogonal filterbanks and rate-distortion algorithms is then discussed as the issue of estimating the reconstruction error as an additive function of the subband distortion. We propose a weighted sum of the subband distortions as an estimate, whose accuracy is calculated by a wide range of experiments. This accuracy is shown to be correlated to the Riesz bounds of the filterbanks. We conclude that from this point of view, most of the usual biorthogonal filterbanks may be considered as nearly orthogonal.

The design of filter banks for source coding purposes classically relies on the perfect reconstruction (PR) property. However, several studies have shown that taking the quantization noise into account in the design could yield a noticeable reduction of the mean square reconstruction error. The purpose of this study is to show that perceptual improvement can also be obtained in the particular audio coding context by relaxing the PR constraint. In this context, the mean square error is not relevant any more, and we define a new perceptual distortion criterion, making use of a simplified ear model, the MPE (mean perceptual error). Then, synthesis filters are optimized so as to minimize this MPE. Finally, this MMPE (minimum MPE) filter bank is included in an audio coding scheme. Compared to the corresponding PR filter bank-based scheme by the means of POM (perceptual objective measure), they show an improved audio quality.

This paper presents source coding schemes, based on both parallel and tree-structured filter banks, in which synthesis filters and quantizers are jointly optimized under bit-rate constraint. The design of reconstruction filter banks thus takes into account the amount of subband quantization noise, and minimizes the output mean square error (MSE). All other constraints on the filters, such as perfect reconstruction or maximum selectivity, are relaxed, and noticeable improvements over perfect reconstruction schemes with optimal bit-rate allocation are shown by means of rate-distortion curves, for both synthetic and audio signals.

We address the issue of choosing an optimal wavelet packets decomposition for low-delay audio bit-rate reduction. The decomposition tree and the choice of the wavelet filters for each 2-band cell of the tree are optimized. For a given filterbank we measure the entropy of the symbols resulting from a quantization stage ensuring transparent compression. This measure is the criterion to be minimized under a delay constraint. The optimization is carried out with simulated annealing techniques among a large family of filters. We show that there is no loss choosing the wavelet filters among a family of filters that have been optimized with respect to coding gain for AR(1) models. This provides efficient wavelet packets for low bit-rate low delay audio compression.

We address optimization and adaptation issues in designing the best wavelet filters for the representation or the compression of a given signal. A signal-based optimization technique is proposed and the application of this technique using different optimization criteria, corresponding to energy compaction, is considered. When applying this strategy to textures, for region-based image compression, we show that significant gain in a rate-distortion sense is achievable: up to 1.2 dB improvement is to be expected when compared to usual efficient filters (optimal in coding gain for AR(1) models). The choice of the optimization criterion is discussed for optimal performances in the rate-distortion sense.

We address the issue of choosing an optimal wavelet packets transform for audio compression. We present a comparison method based on a perceptual approach, which provides an entropic bit-rate for "transparent" coding of a given audio signal. The test with different wavelets leads to the conclusion that the most significant synthesis criterion for audio compression is the so-called "coding gain", while frequency selectivity, regularity and orthogonality seem less relevant.

We study the non-orthogonality of perfect-reconstruction (PR) biorthogonal filter banks by measuring the energy preservation between the spatial and transform domains. The mathematical formulation of that issue leads to the computation of the Riesz constants, and a more relevant modelization leads to a measure of near-orthogonality which is well suited for image compression systems based on filter banks. This provides a criterion for the validity of the energy preservation approximation: we can compare the latter approximation with the one that is made when estimating the perceptual quality of an image by the mean square error.

New solutions to the issue of designing transmitter and receiver filters for data transmission are proposed: We design two different linear-phase FIR filters, a shorter receiver filter and a longer transmitter filter, whose product is a Nyquist filter, with an exactly zero inter-symbol interference (ISI). Holding simultaneously exactly zero ISI and phase linearity is new for an oversampling factor equal to 2. The design algorithm takes into account various frequency specifications. Furthermore, the filters are nearly optimal with reference to signal-to-noise ratio (SNR) and the complexity of the transmission system is reduced. A design chart and several design examples are given which illustrate the capabilities of our approach.